stat709-16 - Chapter 2 Fundamentals of Statistics Lecture...

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logo Chapter 2: Fundamentals of Statistics Lecture 16: Populations, samples, models, and statistics Appilcation One or a series of random experiments is performed. Some data from the experiment(s) are collected. Planning experiments and collecting data (not discussed in the textbook). Data analysis: extract information from the data, interpret the results, and draw some conclusions. Descriptive data analysis Summary measures of the data, such as the mean, median, range, standard deviation, etc., and some graphical displays, such as the histogram and box-and-whisker diagram, etc. It is simple and requires almost no assumptions, but may not allow us to gain enough insight into the problem. UW-Madison (Statistics) Stat 709 Lecture 16 September 2, 2011 1 / 13
logo Chapter 2: Fundamentals of Statistics Lecture 16: Populations, samples, models, and statistics Appilcation One or a series of random experiments is performed. Some data from the experiment(s) are collected. Planning experiments and collecting data (not discussed in the textbook). Data analysis: extract information from the data, interpret the results, and draw some conclusions. Descriptive data analysis Summary measures of the data, such as the mean, median, range, standard deviation, etc., and some graphical displays, such as the histogram and box-and-whisker diagram, etc. It is simple and requires almost no assumptions, but may not allow us to gain enough insight into the problem. UW-Madison (Statistics) Stat 709 Lecture 16 September 2, 2011 1 / 13
logo Statistical inference and decision theory We focus on more sophisticated methods of analyzing data: statistical inference and decision theory . The data set is a realization of a random element defined on a probability space , F , P ) P is called the population . The data set or the random element that produces the data is called a sample from P . The size of the data set is called the sample size . Our task A population P is known iff P ( A ) is a known value for every event A F . In a statistical problem, the population P is at least partially unknown. We would like to deduce some properties of P based on the available sample. UW-Madison (Statistics) Stat 709 Lecture 16 September 2, 2011 2 / 13
logo Statistical inference and decision theory We focus on more sophisticated methods of analyzing data: statistical inference and decision theory . The data set is a realization of a random element defined on a probability space , F , P ) P is called the population . The data set or the random element that produces the data is called a sample from P . The size of the data set is called the sample size . Our task A population P is known iff P ( A ) is a known value for every event A F . In a statistical problem, the population P is at least partially unknown. We would like to deduce some properties of P based on the available sample.

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